Three-dimensional reconstruction from serial sections. IV. The reassembly problem

In many fields of biology and medicine there is a pressing need for quantitative descriptions of biological structures at a resolution of micrometers. This need is currently met best by three-dimensional reconstruction from serial sections. The preliminary steps in three-dimensional reconstruction include fixation, embedding in plastic, introduction of fiducials, serial sectioning, and staining. At the light microscope level, with which we are chiefly concerned, one will usually want to do photomicrography (or videomicrography) of adjacent fields within individual tissue sections. The resultant images are projected onto a digitizer pad and the contours of interest manually digitized. From the digitized coordinates generated thereby, one wishes to generate a likeness of the original object, using computer graphic displays, and to then do interactive morphometrics. The problem of combining the digitized coordinates so as to produce a numerically faithful representation of the original object (i.e., the reassembly problem) is, as a practical matter, nontrivial. A technical description of the reassembly problem is presented. The main factors entering into a solution of the problem are discussed and a mathematical statement of the solution is given.